ABSTRACT
This chapter illustrates the application of the finite difference method (FDM) as well as the finite element method to the incompressible potential flow problems. The origin of the FDM probably traces back to the time of Leibniz and Euler, and subsequently evolved into different techniques. The FDM became more established after 1928 after the Courant-Friedrichs-Lewy stability condition was derived for hyperbolic type partial differential equations. Although for solid mechanics and structural analysis the emergence of the finite element method in 1960 took over the role of finite difference in numerical analysis, in the area of fluid mechanics, the FDM remains a popular choice. There are many different kinds of finite difference schemes. In general it can be classified into explicit and implicit finite difference schemes. The finite element method is a numerical technique for finding approximate solutions to boundary value problems.
